All-optical soliton switching for the asymmetric fiber couplers

Coupled nonlinear Schrödinger (CNLS) equations for the fiber couplers with asymmetric selfphase modulation (SPM) and cross-phase modulation (XPM) are studied. With symbolic computation, oneand two-soliton solutions are obtained for the constantand variable-coefficient CNLS equations. Switching dynamics of the solitons is discussed, and effects of the second-order group-velocity dispersion β2, SPM coefficient σ1, XPM coefficient σ2 and Kerr nonlinear intensity γ on the all-optical switching properties are studied, while other coefficients in those equations are seen not to affect the all-optical switching properties. For the constant-coefficient CNLS equations, we find that |β2| is proportional to the optical switching speed, and the optical extinction ratios increase with the decrease of σ1/σ2 and increase of |β2| and γ. A numerical simulation by the split-step Fourier and Runge-Kutta methods is presented on the constant-coefficient CNLS equations to analyse the stability of the oneand two-solitons with the random initial perturbations. For the variable-coefficient CNLS equations, effects of σ1/σ2, β2(z) = a2e bz and γ(z) = a3e bz on the optical switching are analyzed (where a2, a3 and b are all constants, and z gives the direction of propagation in the fiber couplers): optical switching speed increases with the increase of |a2| and decrease of |b|, and optical extinction ratios increase with the increase of |a2| and decrease of σ1/σ2 and |a3|.